A034954 Odd triangular numbers with prime indices.

3, 15, 91, 153, 435, 703, 861, 1431, 1891, 2701, 4005, 4753, 5151, 5995, 6441, 9453, 11175, 12403, 15051, 16471, 18721, 19503, 26335, 27261, 29161, 33153, 36315, 38503, 39621, 43071, 49141, 50403, 56953, 61075, 62481, 69751, 75855, 79003

Offset: 1

Author

Patrick De Geest, Oct 15 1998

Keywords

• nonn

Comments

For prime indices p such that p(p+1)/2 is 'odd' see A002313 (primes of form 4n+1).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Eric Weisstein's World of Mathematics, Triangular Number

Crossrefs

Cf. A000217, A002313.

Cf. A014493, A034953, A034955.

Programs

Mathematica

Select[Table[Prime[n] (Prime[n] + 1)/2, {n, 500}], OddQ[#] &] (* G. C. Greubel, Nov 03 2017 *)
With[{nn=400},Select[Thread[{Accumulate[Range[nn]],Range[nn]}],OddQ[ #[[1]]] && PrimeQ[#[[2]]]&]][[All,1]] (* Harvey P. Dale, Mar 06 2019 *)

Formula

a(n) = A000217(A002313(n)). - Michel Marcus, Nov 04 2017